Mobility experience with a research focus
PhD sandwich ; Post Doc
Department of Physics and Astronomy (with envisaged collaborations with the PhD Programs in Mathematics of University of Pisa and/or Gran Sasso Science Institute)
The proposed research activities are related to the PRIN Grant 2022NTKXCX “Stochastic properties of dynamical systems”, recently financed by the Italian Ministry of University and Research. Possible research directions include:
Non-compact and infinite-measure preserving dynamical systems. The interest here is both in developing new general ideas and techniques in infinite ergodic theory and deriving stochastic properties of specific systems. Questions in the first group include: limit theorems for Birkhoff sums of global (non-integrable) observables, notions of infinite mixing and their applications (quantitative mixing, decay of correlations, limit theorems), sufficient conditions for the K-property in general systems, etc. Questions in the second group include: ergodic and stochastic properties of aperiodic Lorentz gases (applications of ergodicity, mixing, K-property, decay of correlations, limit theorems) and similar systems, such as expanding/hyperbolic maps on non-compact and/or homogeneous space, possibly with quenched disorder.
Dynamical systems with holes and extreme events. Since the study of dynamical systems with holes/leaks in essentially in its infancy, even basic problems in the field area of interest, e.g., escape rates for general expanding maps, dependence of the escape rate on the position of the hole, the problem of the maximal escape rate, perturbation of holes, etc. Related to this, a direction of interest is that of large deviations in Extreme Value Theory for chaotic dynamical systems (and stochastic processes as well).
Applications to systems of physical interest. The group is especially interested in the following applications of techniques from dynamical systems: “internal-wave billiards”, that is, point-particle systems which approximate the motion of internal or inertial waves in fluid dynamics (main mathematical technique: homeomorphisms of the circle); spectral properties of Koopman and transfer operators for questions of assimilation, interpretation and forecast of data in climate-related problems. Numerical work will also be considered.
The working language of the research group will (mostly) be English.
Doctoral students / postdocs in Mathematics, or Physics and Engineering with a solid background in Mathematics (e.g., Mathematical Physics, Mathematical Engineering, etc.)
PhD sandwich: 6-12
Post Doc: 6-12